Exact boundary controllability and optimal control for a generalised Korteweg de Vries equation

A generalized Korteweg de Vries system is studied and shown to be controllable by boundary control and a nonlinear optimal control problem is replaced by a linear, time-varying sequence of problems which can be solved by classical methods. This is achieved by showing the controllability of a linearized version and then by applying a fixed point argument.. A subtle smoothing property is required which is more complex than the usual smoothing produced by the semigroup of the system. A new approximation technique is then applied to solve the optimal control problem, reducing it to a sequence of linear, time-varying systems.